Portraits or selfie images taken from a close distance typically suffer from perspective distortion. In this paper, we propose an end-to-end deep learning-based rectification pipeline to mitigate the effects of perspective distortion. We learn to predict the facial depth by training a deep CNN. The estimated depth is utilized to adjust the camera-to-subject distance by moving the camera farther, increasing the camera focal length, and reprojecting the 3D image features to the new perspective. The reprojected features are then fed to an inpainting module to fill in the missing pixels. We leverage a differentiable renderer to enable end-to-end training of our depth estimation and feature extraction nets to improve the rectified outputs. To boost the results of the inpainting module, we incorporate an auxiliary module to predict the horizontal movement of the camera which decreases the area that requires hallucination of challenging face parts such as ears. Unlike previous works, we process the full-frame input image at once without cropping the subject's face and processing it separately from the rest of the body, eliminating the need for complex post-processing steps to attach the face back to the subject's body. To train our network, we utilize the popular game engine Unreal Engine to generate a large synthetic face dataset containing various subjects, head poses, expressions, eyewear, clothes, and lighting. Quantitative and qualitative results show that our rectification pipeline outperforms previous methods, and produces comparable results with a time-consuming 3D GAN-based method while being more than 260 times faster.